INVARIANT SETS AND NORMAL SUBGROUPOIDS OF UNIVERSAL ETALE GROUPOIDS INDUCED BY CONGRUENCES OF INVERSE SEMIGROUPS
INVARIANT SETS AND NORMAL SUBGROUPOIDS OF UNIVERSAL ETALE GROUPOIDS INDUCED BY CONGRUENCES OF INVERSE SEMIGROUPS
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逆半群同余导出的通用ETALE群的不变集和正规子群
DOI：
10.1017/s1446788721000021
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发表时间：
2021
影响因子：
0.7
通讯作者：
KOMURA FUYUTA
中科院分区：
文献类型：
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作者：
Makoto Kirimura;Yoko Akiyama;Fuminobu Sato;中村祥司;本田拓海，峪龍一，内田賢悦;川村雄斗，峪龍一，内田賢悦;Seiichro Mizuta;新田翔，峪龍一，内田賢悦;ハスゴワ （哈斯高娃）;峪龍一，内田賢悦;KOMURA FUYUTA
对于给定的逆半群，可以关联一个称为通用群胚的étale群胚。我们的动机是研究逆半群和相关的étale群胚之间的关系。在本文中，我们关注逆半群的同余，这是考虑逆半群商的基本概念。我们证明逆半群的同余可导出一个闭不变集和通用群群的正规子群群。然后我们证明与商逆半群相关的通用群群是通过原始通用群群的限制和商来描述的。最后，我们计算由特殊同余（包括阿贝尔化）引起的不变集和正常子群。
For a given inverse semigroup, one can associate an étale groupoid which is called the universal groupoid. Our motivation is studying the relation between inverse semigroups and associated étale groupoids. In this paper, we focus on congruences of inverse semigroups, which is a fundamental concept for considering quotients of inverse semigroups. We prove that a congruence of an inverse semigroup induces a closed invariant set and a normal subgroupoid of the universal groupoid. Then we show that the universal groupoid associated to a quotient inverse semigroup is described by the restriction and quotient of the original universal groupoid. Finally we compute invariant sets and normal subgroupoids induced by special congruences including abelianization.